On the Lifetime of Wireless Sensor Networks

We demonstrate the applicability of our definition based on the sur-veyed lifetime definitions as well as using some example scenarios to explain the various aspects influencing sensor

On the Lifetime of Wireless Sensor Networks

ISABEL DIETRICH and FALKO DRESSLER

University of Erlangen

Network lifetime has become the key characteristic for evaluating sensor networks in an

application-specific way Especially the availability of nodes, the sensor coverage, and the

con-nectivity have been included in discussions on network lifetime Even quality of service measures

can be reduced to lifetime considerations A great number of algorithms and methods were

pro-posed to increase the lifetime of a sensor network—while their evaluations were always based on a

particular definition of network lifetime Motivated by the great differences in existing definitions

of sensor network lifetime that are used in relevant publications, we reviewed the state of the art

in lifetime definitions, their differences, advantages, and limitations This survey was the

start-ing point for our work towards a generic definition of sensor network lifetime for use in analytic

evaluations as well as in simulation models—focusing on a formal and concise definition of

accu-mulated network lifetime and total network lifetime Our definition incorporates the components

of existing lifetime definitions, and introduces some additional measures One new concept is the

ability to express the service disruption tolerance of a network Another new concept is the notion

of time-integration: in many cases, it is sufficient if a requirement is fulfilled over a certain period

of time, instead of at every point in time In addition, we combine coverage and connectivity to

form a single requirement called connected coverage We show that connected coverage is different

from requiring noncombined coverage and connectivity Finally, our definition also supports the

concept of graceful degradation by providing means of estimating the degree of compliance with

the application requirements We demonstrate the applicability of our definition based on the

sur-veyed lifetime definitions as well as using some example scenarios to explain the various aspects

influencing sensor network lifetime.

Categories and Subject Descriptors: C.2.4 [Computer-Communication Networks]: Distributed

Systems; C.4 [Performance of Systems]— Performance attributes

General Terms: Performance

Additional Key Words and Phrases: Sensor networks, lifetime, connectivity, coverage, longevity

ACM Reference Format:

Dietrich, I and Dressler, F 2009 On the lifetime of wireless sensor networks ACM Trans Sen.

Netw 5, 1, Article 5 (February 2009), 39 pages DOI= 10.1145/1464420.1464425 http://doi.acm.org/

10.1145/1464420.1464425

Authors’ address: University of Erlangen, Department of Computer Science 7, Martensstr 3, 91058

Erlangen, Germany; email: {isabel.dietrich,dressler}@informatik.uni-erlangen.de.

Permission to make digital or hard copies of part or all of this work for personal or classroom use

is granted without fee provided that copies are not made or distributed for profit or commercial

advantage and that copies show this notice on the first page or initial screen of a display along

with the full citation Copyrights for components of this work owned by others than ACM must be

honored Abstracting with credit is permitted To copy otherwise, to republish, to post on servers,

to redistribute to lists, or to use any component of this work in other works requires prior specific

permission and/or a fee Permissions may be requested from Publications Dept., ACM, Inc., 2 Penn

Plaza, Suite 701, New York, NY 10121-0701 USA, fax +1 (212) 869-0481, or permissions@acm.org.

C

 2009 ACM 1550-4859/2009/02-ART5 $5.00 DOI 10.1145/1464420.1464425 http://doi.acm.org/

10.1145/1464420.1464425

1 INTRODUCTION

With the proliferation of wireless sensor networks (WSN), completely new plication domains for wireless ad hoc networks have emerged From wildlifemonitoring and precision agriculture to habitat monitoring and logistics ap-plications, there is an increasing demand for developing more efficient sensornetworks Especially the characteristic features of WSN, such as the limita-tions in the available resources (energy, processing speed, storage), distinguishsensor networks from other ad hoc networks [Culler et al 2004] Besides theserestrictions, WSN are also exposed to various requirements, for example thevarying density of the node deployment, and possibly hazardous environmentalconditions [Chong and Kumar 2003] Many aspects concerning sensor networkshave already been investigated [Akyildiz et al 2002a], for example routing anddata dissemination schemes [Akkaya and Younis 2005], self-organization issues[Dressler 2008], the efficient deployment of sensor nodes [Bai et al 2006], andthe interaction of sensor and actor networks (SANETs) [Akyildiz and Kasimoglu2004], while others are still works in progress This includes the study of

ap-network lifetime as a key characteristic of WSN.

Network lifetime is perhaps the most important metric for the evaluation

of sensor networks Of course, in a resource-constrained environment, the sumption of every limited resource must be considered However, network life-time as a measure for energy consumption occupies the exceptional positionthat it forms an upper bound for the utility of the sensor network The networkcan only fulfill its purpose as long as it is considered alive, but not after that

con-It is therefore an indicator for the maximum utility a sensor network can vide If the metric is used in an analysis preceding a real-life deployment, theestimated network lifetime can also contribute to justifying the cost of the de-ployment Lifetime is also considered a fundamental parameter in the context

pro-of availability and security in networks [Khan and Misic 2008]

Network lifetime strongly depends on the lifetimes of the single nodes thatconstitute the network This fact does not depend on how the network life-time is defined Each definition can finally be reduced to the question of whenthe individual nodes fail Thus, if the lifetimes of single nodes are not pre-dicted accurately, it is possible that the derived network lifetime metric willdeviate in an uncontrollable manner It should therefore be clear that accu-rate and consistent modeling of the single nodes is very important However,

a detailed discussion of all the different approaches found in the literature

is beyond the scope of this article The lifetime of a sensor node basicallydepends on two factors: how much energy it consumes over time, and howmuch energy is available for its use Following the discussion by Akyildiz et al.[2002b], the predominant amount of energy is consumed by a sensor node dur-ing sensing, communication, and data processing activities A sensor networkconsists of a number of these nodes In such a network, the nodes communi-cate to form an ad hoc network and are thus able to transmit the collectedsensor data to designated sinks In principle, this is also true if in-networkprocessing mechanisms are employed [Dressler et al 2007; Krishnamachari

et al 2002]

Lifetime studies first came up because the recharging or replacement of teries is not feasible in many scenarios (too many nodes, hostile environment,etc.), and thus the lifetime of the network cannot be extended infinitely Natu-rally, lifetime was then discussed from different points of view, which led to thedevelopment of various lifetime metrics Depending on the energy consumersregarded in each metric and the specific application requirements considered,these metrics may lead to very different estimations of network lifetime.

bat-In summary, it can be said that although network lifetime is considered asone of the most important parameters for evaluating sensor networks or foralgorithms to be used in sensor networks, there are still a large number ofopen issues This finally motivated us to work on a general definition for sensornetwork lifetime that can be directly applied in analytical evaluation processes

as well as in simulation models

In this article, we discuss the need to refer tonetwork lifetime as the key

characteristic to evaluate the performance of sensor networks We show thatessentially all parameters can be reduced to lifetime considerations Such pa-rameters include coverage, connectivity, and node availability Based on theanalysis of previous lifetime definitions, we propose a more concise definitionthat can be used in all domains of sensor network research Our model in-cludes formal definitions of the lifetime aspects found in the surveyed papers,along with a number of new concepts First, we introduce service disruptiontolerance, which describes the ability of the network to cope with temporaryfailures of one or more of its requirements Second, a time-integrated require-ment specifies that it does not have to be satisfied at each point in time, butrather in the course of a certain time interval Third, we introduce connectedcoverage as a combination of coverage and connectivity and show that this is

a different requirement than connectivity and coverage on their own Finally,our model inherently supports the concept of graceful degradation For this,

we provide means of estimating the degree of compliance with the tion demands The primary contributions of this article can be summarized asfollows:

applica-—Analysis of existing lifetime definitions (Section 2) In this section, we provide

a survey on network lifetime definitions as well as a comparison based onthe selected parameters

—Overview of the parameters influencing network lifetime (Section 3) We

sum-marize all parameters that affect the lifetimes of single nodes as well asthe overall network lifetime It will become obvious that application require-ments have to be used to reflect the particular lifetime measures

—Concise redefinition of network lifetime (Section 4) We conclude the survey

and the listed requirements with a formal definition of network lifetime thatreflects all needed characteristics of typical sensor networks Next to thewell-known requirements such as node availability, coverage, or connectivity,

we introduce the concepts of service disruption tolerance, time-integration,connected coverage, and graceful degradation We also show how to includeother measures such as the network quality, in the definition

The developed metrics for network lifetime can be used to evaluate algorithmsand methods in a comparable way, if the parameters used in the specific sce-nario are published Lower bounds for specific parameters can be provided forestimating the degree of compliance with the application demands.

The remainder of the article is organized as follows A survey of lifetimedefinitions is provided in Section 2 Afterwards, we discuss open issues andmissing features in these lifetime definitions in Section 3 In Section 4, wepresent our more concise definition for sensor network lifetime Its applicability

is demonstrated in Section 5, based on the survey of lifetime definitions, as well

as on an example Finally, Section 6 concludes the article

2 RELATED WORK ON NETWORK LIFETIME

In the literature, we can find a great number of relevant publications thataddress the problem of sensor network lifetime Some papers employ network

lifetime as a criterion that needs to be maximized, but never exactly definethe term network lifetime However, the majority of authors do state how net-work lifetime is defined in the context of their work Obviously, this leads to

a strong diversity of coexistent definitions In this section, we summarize themost common definitions in the form of a survey of lifetime definitions

2.1 Network Lifetime Based on the Number of Alive Nodes

The definition found most frequently in the literature isn-of-n lifetime In this

definition, the network lifetimeT nends as soon as the first node fails, thus

T n n= min

v ∈V T v,withT vbeing the lifetime of nodev Some authors exclude the sink nodes from

the node setV to reflect the assumption that a power plug is available at the

sink nodes [Madan et al 2005] T n is a very convenient definition It is easy

to compute and the algorithms running in the network do not have to dealwith topology changes This is because in a network without mobile nodes—which is by far the most common case considered at the moment—the firstnode to fail results in the first topology change after the deployment However,

in most cases the lifetime calculated by this metric will be far too short formeaningful evaluation of sensor network applications For example, consider anode that has several direct neighbors with the same sensing equipment Mostnetworks will be able to cope with the failure of one node in such a case but themetric cannot represent this kind of network redundancy Therefore, the onlycase in which this metric can be reasonably used is if all nodes are of equalimportance and critical to the network operation, as stated by Madan et al.[2005]

If n-of-n lifetime is to be used as a comparative metric, another objection

usually holds This definition favors WSN algorithms that ensure a maximumlifetime for each node: where the first node dies last This means that algorithmsthat deplete the given energy most uniformly (where therefore most remainingnodes fail shortly after the first one) are possibly assigned a longer lifetime than

those algorithms where a node may fail relatively early, but the network can stillprovide useful information for a long time after this event TheT n nmetric is alsonot adequate for evaluating scenarios that consider hardware failures, becauserandomly distributed hardware failures might occur very early and thus distortthe lifetime measure considerably In spite of these arguments, many authors,for example, Wang et al [2005], and Chang and Tassiulas [2000, 2004], adoptthis metric without further consideration Mhatre and Rosenberg [2004] statethatn-of-n lifetime might be a conservative approach, especially for a system

with single-hop communication

A common variant of theT nmetric defines the network lifetime as the timeuntil the fraction of alive nodes falls below a predefined threshold,β, or the time

during which at leastk out of n nodes are alive (k-of-n lifetime T k) While thismetric is better thann-of-n lifetime, it still lacks accuracy Consider the case

whenk< k nodes at strategic positions (perhaps around the base station) fail

and the remaining nodes now have no possibility of transmitting any data tothe sink Then the network should not be considered alive, but the metric doesnot recognize this until anotherk − k nodes have failed Again, comparative

evaluations cannot be performed using this metric as no statements are made

as to where the nodes fail and whether the remaining nodes are still able totransmit data to the sink, or to sense events in the region of interest [Deng

et al 2005]

Hellman and Colagrosso [2006] define another metric based on the number

of available nodes They divide the set of nodes into critical and non-criticalnodes and then allow for k node failures in the group of non-critical nodes

and no failures at all in the group of m critical nodes They name this

ap-proachm-in-k-of-n lifetime Nevertheless, the objections as stated for k-of-n still

apply

Another variant of n-of-n lifetime is discussed in the context of

cluster-ing schemes [Chiasserini et al 2002; Soro and Heinzelman 2005] An tant assumption for these approaches is that the cluster heads are chosenbeforehand—probably as a set of special, more powerful nodes—and remainunchanged throughout the network lifetime Then they define network lifetime

impor-as the time until the first cluster head fails (n-of-n cluster heads) This approach

is very limited, as in most clustering schemes, cluster heads vary dynamically

to balance the load between homogeneous nodes In addition, all the constraintsfrom the discussion ofn-of-n lifetime also apply here.

Finally, it is possible to define network lifetime as the time until all nodeshave been drained of their energy This metric is very rarely used, for example inTian and Georganas [2002], and then only as a best-case metric in combinationwith other metrics This is due to the fact that the metric is far too optimistic

to be useful In most cases, a sensor network stops providing any useful service

a long time before the last node finally fails

In summary, it is evident that defining network lifetime solely based on thenumber of alive nodes is insufficient because neither the ability to communi-cate measurements nor the ability to sense events in the region of interest areincorporated into these metrics

2.2 Network Lifetime Based on Sensor Coverage

Considering the specific characteristics of sensor networks, measuring the work lifetime as the time that the region of interest is covered by sensornodes seems to be a natural way to define the lifetime Coverage can be de-fined in different ways, depending on the composition of the region of interestand the achieved redundancy of the coverage The region of interest can be

net-a two-dimensionnet-al net-arenet-a or net-a three-dimensionnet-al volume where enet-ach point side the area or volume has to be covered This is often referred to as area orvolume coverage If only a finite set of target points inside an area has to becovered, the corresponding coverage problem is called target coverage A thirdcoverage problem, barrier coverage, describes the chance that that a mobiletarget can pass undetected through a barrier of sensor nodes [Cardei and Wu2004]

in-There are two approaches to describe the degree of coverage redundancythat can be achieved by a given sensor network The first approach requiresthat only a given percentageα, of the region of interest, is covered by at least

one sensor This is commonly calledα-coverage The second approach aims to

achieve more redundancy, and thus requires that each point within the region

of interest is covered by at leastk sensors This is termed k-coverage.

Several papers base their definitions of network lifetime on a coverage ant Among these, the most common definition uses 1-coverage to define thelifetime as the time that the region of interest is completely within the sensingrange of at least one sensor node—the region is covered by at least one node.This definition is adopted for target coverage in Cardei et al [2005], and Liu

vari-et al [2005b] and for area coverage in Bhardwaj vari-et al [2001], and Bhardwajand Chandrakasan [2002]

A less strict variant of this definition is that only a fraction,α, of the region

of interest needs to be covered This definition can be found for example in Wu

et al [2005], Ye et al [2002], and Zhang and Hou [2005a] A stricter variantdemanding that each point is covered by at leastk nodes is adopted for example,

in Mo et al [2005]

Sensor coverage is often argued to be the most important measure for thequality of service a sensor network provides There is a lot of ongoing researchconcerning coverage in sensor networks, often in the context of deploymentstrategies or scheduling algorithms Good surveys can be found for example,

in Cardei and Wu [2004] and Huang and Tseng [2005] However, defining work lifetime solely based on the achieved coverage is not sufficient for mostapplication scenarios because it is not guaranteed that the measured data canever be transmitted to a sink node

net-2.3 Network Lifetime Based on Connectivity

Another group of metrics takes the connectivity of the network into account.Connectivity is a metric that is commonly encountered in the context of ad hocnetworks because there is no notion of sensor coverage in ad hoc networks andthus the ability to transmit data to a given destination is most important The

definition for ad hoc network lifetime given by Blough and Santi [2002] definesthe lifetime as the minimum time when either the percentage of alive nodes orthe size of the largest connected component of the network drop below a spec-ified threshold However, this definition only considers the size of the largestconnected component in the network This is clearly insufficient in WSNs whereconnectivity towards a base station is what matters most This is reflected byCarbunar et al [2006], who define connectivity as the percentage of nodes thathave a path to the base station.

Baydere et al [2005] and Yu et al [2001] define the network lifetime in terms

of the total number of packets that could be transmitted to the sink While thisnumber can serve as an indicator for the persistence of the network, it is verydependent on the actual algorithms used in the network If, for example, dataaggregation algorithms are used, the number of packets to be transmitted to thesink is reduced However, these aggregated packets contain the same degree ofinformation as the much higher number of non-aggregated packets Therefore,the applicability of this metric in comparing the lifetimes of different networksetups is limited Especially when data aggregation algorithms are employed,this metric loses much of its expressive power Another drawback is that thenumber of transmitted messages gives no clue as to how long, in time units,the network was able to measure its environment Even if the traffic patternproduced by the sensing application is known, no conclusions can be drawnabout the absolute lifetime because the pattern can be modified by packet loss

or data aggregation Similar considerations hold for in-network data processing[Dressler et al 2007]

A third metric aiming at network connectivity defines the network lifetime interms of the number of successful data gathering trips Olariu and Stojmenovic[2006] In Giridhar and Kumar [2005] this is further confined to the number

of trips possible “without any node running out of energy.” This statement fectively reduces the definition ton-of-n lifetime, the difference being only that

ef-the lifetime is not given in time units, but in ef-the number of data gaef-theringtrips So, in addition to the drawbacks described forn-of-n lifetime, the draw-

backs for the definition based on the total number of transmitted packets alsoapply

Integrating connectivity in a network lifetime metric is certainly a good idea.However, it is important to consider connectivity towards a base station, notjust connections between arbitrary sensor nodes In addition, measuring thelifetime of a connected network in terms of numbers of transmitted packets

is not comparable across different networks, and gives no indication of theabsolute network lifetime

2.4 Network Lifetime Based on Sensor Coverage and Connectivity

Due to the described limitations, several authors combine the coverage-basedmetrics with connectivity metrics The network lifetime metric as defined inWang et al [2003] and Xing et al [2005] gives the time when either the coverage

or the connectivity drops below a predefined threshold In this case, coverage is

measured in terms ofα-coverage as discussed before Connectivity is measured

in terms of the packet delivery ratio at the sink node

Some authors completely hide details of their definition [Mhatre et al 2005;Sha and Shi 2005; Cardei and Wu 2004] and define network lifetime for example

as “the time interval that the network can perform the sensing functions andtransmit data to the sink” [Cardei and Wu 2004] In other terms, networklifetime is defined to be the time until either coverage or connectivity is lost Theexact definition of coverage and connectivity is left unspecified Mhatre et al.[2005] do not measure the lifetime in traditional time units, but in the number

of successful data gathering trips We have already discussed the disadvantages

of this approach

Another interesting analysis of network lifetime can be found in a paper by

Mo et al [2005] They define lifetime as the expectation of the interval duringwhich the probability that connectivity and k-coverage are guaranteed is at

leastβ At that point, there are no big differences from the other approaches in

this section However, in contrast to most other definitions, Mo et al [2005] allowfor the variation of sensing ranges between sensor nodes This is an importantcharacteristic, as it is not to be expected that the sensing ranges in real-worlddeployments have exactly the same size on all the nodes

2.5 Network Lifetime Based on Application Quality of Service Requirements

A number of researchers define network lifetime solely in terms of the plication quality of service requirements We appreciate this approach, espe-cially when considering the fact that every design decision in a sensor networkcompletely depends on the specific application the network is designated toperform

ap-For example, Kumar et al [2005] state “We define the lifetime of a WSN to

be the time period during which the network continuously satisfies the tion requirement.” Nevertheless, this illustrates the most important drawback

applica-of such a formulation; it is too abstract to be applica-of any use in practical studies applica-ofWSNs Although it covers every possible aspect by putting it all into the appli-cation requirements, the possible characteristics of application requirementsare left unspecified

Another definition in this domain is the time until “the network no longerprovides an acceptable event detection ratio.” as stated by Tian and Georganas[2002] Although this definition is also quite vague, it does specify one applica-tion requirement, namely that of a specified ratio of event detections However,the detection of events does not necessarily include the transmission of a corre-sponding report to a sink node The definition therefore lacks a characteristicthat is important for most sensor networks

2.6 Network Lifetime as Defined by Blough and Santi

One definition of sensor network lifetime, namely that of Blough and Santi[2002], seems to provide a more concise meaning for the term than most others.They define the lifetime of a sensor network as the minimum of three points

in time, each parameterizable with a constant (0≤ c1,c2,c3 ≤ 1) to allow forflexible mappings of application requirements The first time point,t1, indicatesthe loss of connectivity in the network Formally,t1is the time it takes for thecardinality of the largest connected component ofG(t) to drop below c1× n(t),

whereG(t) is the communication graph of the network at time t, and n(t) is the

number of alive nodes at timet The second time point, t2, indicates how manynodes are still functional at timet, or more exactly, t2is the time it takes forn(t)

to drop belowc2× n(0) The third time point, t3, states the loss ofα-coverage.

t3is the time it takes for the volume covered to drop belowc3× l d, assuming aregion of interest of the formR = [0, l] d, withd ∈ {1, 2, 3}

So, in this definition, three aspects are combined to form one flexible measure

of network lifetime: the number of alive nodes, connectivity, and coverage Each

of the three aspects can be left out by setting its corresponding parameter tozero

Unfortunately, the definition also has its limitations The coverage aspect,although very flexible in allowing a volume to be covered (and not just a two-dimensional area), does not allow for the possibility of covering only a set oftarget points While target coverage could be reduced to volume coverage (bydefining the region of interest as the smallest volume that includes all pointsfrom the target set), this would mean that the network has to cover a lot ofempty space between the target points that could be ignored otherwise Theconnectivity aspect only defines connectivity within the largest connected com-ponent of the communication graph This does not necessarily include the sinknodes So, with this definition of connectivity, the sink nodes could be oblivious

to the events measured in the network after only a small number of nodes nearthe sink have failed and the remaining network still forms a large enough con-nected component Finally, the definition includes no notion of mobility in thenetwork This can seriously affect the lifetime of a network and the evaluation

of the network lifetime in a performance metric All issues concerning mobilityare discussed in more detail in the next section

2.7 Summary

In summary, we provide a list of the discussed network lifetime definitions,each with a short outline of the definition and selected references that use orpropose this definition in the literature:

(1) the time until the first sensor is drained of its energy [Chang and Tassiulas2000; Duarte-Melo and Liu 2002; Giridhar and Kumar 2005; Lee et al.2004; Madan et al 2005; Mhatre and Rosenberg 2004; Shah and Rabaey2002; Wang et al 2005];

(2) the time until the first cluster head is drained of its energy [Chiasserini

et al 2002; Soro and Heinzelman 2005];

(3) the time there is at least a certain fraction β of surviving nodes in the

network [Cerpa and Estrin 2004; Deng et al 2005; Duarte-Melo and Liu2002; Hellman and Colagrosso 2006; Tilak et al 2002; Wieselthier et al.2002];

(4) the time until all nodes have been drained of their energy [Tian andGeorganas 2002];

(5) k-coverage: the time the area of interest is covered by at least k nodes [Mo

(a) the accumulated time during which at leastα portion of the region is

covered by at least one node [Zhang and Hou 2005a, 2005b, 2005c];(b) the time until the coverage drops below a predefined thresholdα (until

last drop below threshold) [Wu et al 2005; Ye et al 2002];

(c) the continuous operational time of the system before either the erage or delivery ratio first drops below a predefined threshold [Wang

cov-et al 2003; Xing cov-et al 2005; Carbunar cov-et al 2006];

(8) the number of successful data-gathering trips [Giridhar and Kumar 2005;Mhatre et al 2005; Olariu and Stojmenovic 2006];

(9) the number of total transmitted messages [Baydere et al 2005; Yu et al.2001];

(10) the percentage of nodes that have a path to the base station [Carbunar

ap-et al 2002; Wieselthier ap-et al 2002];

(15) min(t1,t2,t3) witht1: time for cardinality of largest connected component

of communication graph to drop belowc1× n(t), t2: time forn(t) to drop

belowc2× n, t3: time for the covered volume to drop belowc3× l d [Bloughand Santi 2002]

3 OPEN ISSUES AND GENERAL REQUIREMENTS

None of the discussed definitions of network lifetime reflects all the tion demands and environmental influences Typically, the real network life-time is approximated under a set of very specific conditions Therefore, theexisting definitions are not applicable in a general context but in networksthat meet the specified conditions However, there are many more parameters

applica-Table I Summary of Requirements Influencing Network Lifetime

Mobility

—complicates analysis of network lifetime [Blough and Santi 2002]

—improves sensor coverage [Batalin and Sukhatme 2002, 2003; Liu et al 2005a; Low et al 2005]

—improves network connectivity [Cerpa and Estrin 2004; Wang et al 2005]

—influences clustering [Bandyopadhyay and Coyle 2003]

—mobile sinks or mobile relays [Gandham et al 2003; Jiang and nan 2004; Wang et al 2005]

Manivan-—combined effects [Dressler and Dietrich 2006]

Heterogeneity

—Some nodes have more battery power [Duarte-Melo and Liu 2002; man and Colagrosso 2006; Lee et al 2004; Liu et al 2005a; Mhatre and Rosenberg 2004; Mhatre et al 2005; Soro and Heinzelman 2005]

Hell-—The amount of data each node must communicate varies [Hellman and Colagrosso 2006; Younis et al 2004]

—Nodes may have different types of sensors [Welsh et al 2003]

—Sensing radius is variable/some nodes have larger sensing radii [Lee et al 2004; Lazos and Poovendran 2006; Mo et al 2005; Zhang and Hou 2005a]

—Some nodes have higher processing power and memory capacity [Lee et al 2004; Soro and Heinzelman 2005]

—Some nodes have longer transmission ranges/transmission range is able [Mhatre and Rosenberg 2004; Xing et al 2005]

vari-—The transmission power varies [Zhou et al 2006]

Application

characteristics —distribution of subtasks

—destination for data packets

—node activity (sensing, processing, communication): by event, by request, regular intervals [Akyildiz et al 2002b]

Quality of

service —general issues [Younis et al 2004; Iyer and Kleinrock 2003]

—collective QoS parameters [Chen and Varshney 2004]

—results not comparable because of incompatible lifetime definitions

influencing sensor network lifetime than just the aspects included in the ing definitions

exist-These parameters are outlined in the following Additionally, we provide

a short overview of the most important requirements in each category inTable I, together with some pointers to the literature, in order to summarize ourdiscussion

3.1 Node Mobility and Topology Changes

At the moment, most authors only consider networks with stationary sensornodes Some consider mobility as a chance for improving network functionality.Others also state that large-scale mobility complicates matters a lot This in-dicates that mobility is indeed a very controversial subject in sensor networks

It offers chances as well as risks for the functionality of the network However,whether chances or risks prevail, it should be clear that it is important to takemobility into account even in a stationary network

The first reason we can give for this is that mobility can be simply regarded

as a series of topology changes With the movement of a node, some networklinks can break, others can be established, and the covered area may be altered

In turn, every topology change can be seen as a special case of mobility As anexample, consider node failures: some network links break when a node fails,and the area covered by sensors is altered in some way The effects are nearlythe same as with traditional mobility: node movements So, even if the nodesthemselves have no possibility of moving on their own, the network should beexpected to be able to cope with node failures

Another reason is that in every real-world deployment, there is an ronment that affects the network in some way Sensor nodes may roll down ahill or be moved—whether on purpose or accidentally—by external forces, forexample, by animals kicking at them These two examples, node failure andaccidental mobility, demonstrate that mobility—topology changes—can occureven in a stationary network A network that cannot cope with mobility at allwill probably face a very short lifetime—and a definition of network lifetimethat does not explicitly account for mobility at all will probably create wronglifetime estimations

envi-The fact that node mobility and topology changes can complicate the analysis

of network lifetime has already been mentioned by Blough and Santi [2002].Consider one of the abstract definitions of lifetime, the definition by Kumarthat measures lifetime as the time period during which the network continu-ously satisfies the application requirement For example, what is the networklifetime if the network is considered alive from a starting time t0 until time

t1, not alive until timet2, alive again until timet3, and not alive after that?

Is it the time until t1? Is it the sum of all the time periods during which thenetwork is alive: the sum oft1− t0andt3− t2? Or is it the time untilt3? Bloughand Santi do not provide a solution for this question We address this issue inSection 4

In the literature, several approaches have been discussed to improve networkbehavior using mobility Several authors investigate the improvement of sensorcoverage over time by exploiting node mobility, for example, if there are notenough static nodes to cover the region of interest [Batalin and Sukhatme 2002;Batalin and Sukhatme 2003; Liu et al 2005a; Low et al 2005; Bisnik et al.2006] Others claim that mobile nodes can improve network connectivity bycarrying data from one part of the network to another [Cerpa and Estrin 2004;Wang et al 2005] The influence of mobility on clustering algorithms is surveyed

in Bandyopadhyay and Coyle [2003] The effects on networks with mobile sinks

or mobile relays are studied for example in Gandham et al [2003], Jiang andManivannan [2004], and Wang et al [2005] Even combined effects have beenstudied, such as the optimization of coverage and network lifetime using virtualmovements, for example, dynamic node reprogramming [Dressler and Dietrich2006].

3.2 Heterogeneity

About one-third of the papers reviewed for this survey do not state whetherthey consider homogeneous or heterogeneous nodes While it is probably safe

to assume that the authors are exploring homogeneous networks in these cases,

it shows that the current level of awareness for node heterogeneity leaves a lot

of room for improvement Most of the authors dealing with heterogeneous nodesconcentrate on just one type of heterogeneity However, a short literature studyrevealed at least eight to ten types of heterogeneity that could have a significantimpact on the functionality and lifetime of sensor networks

The most common type of heterogeneity found in the literature today fies the nodes in the network in two categories depending on their battery power.Most of the nodes are assumed to have a regular amount of energy, while a fewnodes have a significantly larger energy reservoir at their disposal (or evenunlimited energy) This type is mentioned for example in Duarte-Melo and Liu[2002], Hellman and Colagrosso [2006], Lee et al [2004], Liu et al [2005b],Mhatre and Rosenberg [2004], Mhatre et al [2005], and Soro and Heinzelman[2005] Many authors consider this in the context of clustering schemes, wherethe more powerful nodes are assumed to permanently perform the role of clus-ter heads An important observation in this context is that nodes can becomeheterogeneous in terms of battery power simply because of differences in thedischarge behavior of their batteries, depending on environmental factors, forexample temperature differences in the region of the deployment

classi-Another variant is to presume that some nodes have to send a larger amount

of data than others, for example because of different sensor types, as mentioned

in Hellman and Colagrosso [2006] and Younis et al [2004] If the amount of data

is the only criterion of interest, this type can be mapped to heterogeneity in theavailable battery power

However, if sensor coverage is of importance, the different sensor types have

to be considered explicitly because the coverage requirements have to be filled by each type of sensor Nodes with different types of sensors are considered

ful-in Welsh et al [2003] In Lee et al [2004], Lazos and Poovendran [2006], Mo

et al [2005], and Zhang and Hou [2005a], nodes with varying sensing ranges,either due to environmental variations or due to sensor characteristics andsensor types are considered

Powerful nodes with higher processing power and memory capacity are sidered by Lee et al [2004] and Soro and Heinzelman [2005] They also considernodes with different energy levels, which is reasonable because more powerfulnodes, in terms of processing and memory, will usually be preferred as routers

con-or data aggregatcon-ors In that case, mcon-ore powerful batteries are often provided

as well

Varying transmission ranges are considered in Mhatre and Rosenberg[2004], Xing et al [2005], and Zhou et al [2006] Mhatre and Rosenberg [2004]assume that some nodes (the cluster heads) will be capable of long-range trans-missions reaching the base station in a single hop In contrast, Xing et al [2005]consider homogeneous nodes where the transmission ranges can vary and takeirregular shapes due to environmental conditions Zhou et al [2006] take a sim-ilar approach and develop models to treat radio irregularity They also considervarying transmission powers, resulting in varying transmission ranges, as atype of heterogeneity.

Sometimes, mobility is classified as a kind of heterogeneity as well We cussed mobility issues in the previous section

dis-Taking into account all these different sources of heterogeneity in a sensornetwork, it should be obvious why it is important to consider heterogeneity forthe analysis of network lifetime Heterogeneous nodes can have an influence onnetwork lifetime in many ways For example, the lifetime could be prolonged bythe network backbone that is provided by the more powerful nodes The lifetimecould also be shortened if some nodes gather much more data than others andthen fail earlier due to necessary radio activity Heterogeneity can also have aninfluence on the applicability of algorithms, especially of clustering schemes

3.3 Application Characteristics

The application is the driving force of any sensor network However, it is useful

to distinguish between the overall application that a sensor network is madefor, like monitoring environmental parameters in a building, and the programsrunning on each single sensor node For example, it might benefit the overallapplication to split its duties into several tasks that are performed by differ-ent nodes This leads to a heterogeneity of tasks in a network Consider, forexample, a number of nodes sensing temperature values and sending them to alocal destination In this example, the local destination is just another node foraggregating the data and for further forwarding to the base station This ap-proach is especially useful if the individual nodes do not have enough resources

to perform both tasks simultaneously In that case, the lifetime of the networkstrongly depends on the network’s ability to provide an adequate distribution

of all necessary tasks over the available sensor nodes [Dasgupta et al 2003;Krishnamachari et al 2002]

The destination for data packets that is used by the individual sensor nodescan affect communication patterns in the network In addition to the simplecases with single fixed destinations either in the middle or at the edge of thenetwork, multiple destinations at different places or even mobile sinks need to

be considered as well All variants potentially lead to different communicationpatterns in different regions of the network, thus influencing energy consump-tion This effect has been studied for example in Solis and Obraczka [2004].The final and possibly most important factor influencing network lifetime

at the application level is the node activity in terms of sensor measurements,data processing, and communication [Akyildiz et al 2002a] In all cases, theactivity can be triggered by events, for example, sending of data because sensor

measurements exceed some threshold, it can be carried out at regular intervals,

or it can be initiated by a request from another node The frequency of consuming actions will probably be quite different in the three cases

energy-3.4 Quality of Service

It has already been stated that the application is the driving force of every sor network It is to be expected that each application has different demands

sen-on the required services in the network and their quality of service parameters

A definition of network lifetime should take the QoS requirements of the plication into account Consequently, this leads to the central question of whatthe most common application requirements in sensor networks are While thequality of service parameters for traditional networks have been thoroughlystudied, there has been relatively little work on this topic in the context of sen-sor networks, for example, Chen and Varshney [2004] and Younis et al [2004].Traditional QoS measures include the delay (the response time and its com-ponents: transmission times, propagation delays, processing times, queuing de-lays, idle times), the jitter (the delay variation), the throughput and bandwidth,the loss and error rates (packet errors, bit errors), the resource consumption(processing, memory, bandwidth, power), the reliability (MTTF: mean time tofirst failure) and availability (downtime), and the overall costs (total cost of own-ership, return on investment) The QoS requirements of sensor networks can

ap-be different from these traditional measures End-to-end QoS measures are not

as important as collective parameters For example, Chen and Varshney [2004]state, “collective latency is defined as the difference between the time at whichthe first packet related to this event is generated by the source sensors and thetime at which the last packet related to this event or the last packet used tomake a decision arrives at the sink.”

Examples for additional QoS measures being, cited as important for sensornetworks are the coverage, event detection ratio, and exposure (often stated

as the main QoS parameters for sensor networks), connectivity (availability,latency, loss), requirements for continuous service (service disruptions up to alength ofn are tolerated, indicates mission-criticality), the observation accuracy

(measurement errors), and the optimum number of sensors sending informationtoward information-collecting sinks [Chen and Varshney 2004; Younis et al.2004; Iyer and Kleinrock 2003] Many of these parameters already appeared

in the lifetime discussion We see a deep relation between lifetime and quality

of service in sensor networks Therefore, we will integrate QoS directly in ourlifetime definition

3.5 Completeness

Most of the existing lifetime definitions fail to consider multiple important pects of sensor networks in a single step For example, connectivity and cover-age are often investigated independently, whereas these measures essentiallyinfluence each other In general, we also agree on the advantage of analyzingspecific application demands independently for a better understanding of theparticular effects Nevertheless, if different definitions are used that cannot be

as-brought together in a final evaluation step, results become incomparable This

is a serious problem in sensor network research Although it could be tempting

to formulate a new definition of lifetime for each new network, this would tainly be less flexible and less comparable than a single definition incorporatingmany common application requirements

cer-4 A MORE CONCISE DEfiNITION

Based on the survey of lifetime definitions and the corresponding discussion ofopen issues, we now formulate our own definition in this section The overallobjective is to develop a definition that can be parameterized according to theapplication requirements but that also provides comparability between differ-ent optimization efforts of algorithms and methods in WSNs

4.1 Prerequisites

The region of deployment is described by R There can be different definitions

forR, although the concrete specification is not relevant for the definition of

net-work lifetime Some possibilities include a rectangle (R = [0, a1]×[0, a2],|R| =

Y i ⊂ Y It is important to note that each sensor node is associated to a subset

of the set of sensor types This means that there may be more than one sensor

on a node, and there may also be zero sensors on a node The total number ofavailable sensor nodes isn.

U (t) ={u | u ∈ S Y ∧ u alive at t}, |U(t)| = u(t). (3)Now we can define the set of nodes that are active at a timet, as V (t) For

a node to be active, it has to be alive (thereforeV (t) is a subset of U (t)), and it

must not be in a sleep state

V (t) ={v | v ∈ U(t) ∧ v active at t}, |V (t)| = v(t). (4)The set of of nodes that are active at any time in the time interval [t − t, t]

is denoted asW (t) If t is zero, W (t) equals V (t).

W (t) ={w | w ∈ S Y ∧ w active at any t ∈ [t − t, t]}, |W (t)| = w(t). (5)The set of sink nodes or base stations B(t) is defined to be a subset of the

existing nodes S Y In some network settings, sink nodes might be ordinary

sensor nodes acting as base stations for other nodes For this reason, the nition retains the possibility for a sink node to fail or sleep just like any othernode The set of sink nodes may vary over time, and it is also possible that thereare no sink nodes present in the network at some point in time.

defi-B(t) = {b1, , b k } ⊂ S Y (6)The communication graph of the network at a timet, is given as the undi-

rected graphG(t) = (V (t), E(t)) This definition assumes that communication

between two nodes is always possible in both directions Apart from that, noassumptions are made about the communication ranges of the nodes Note thatonly active nodes from the setV (t) are included in the communication graph.

In order to express the ability of two arbitrary nodes,m i andm j, to cate at a timet, it is necessary to check if there exists a series of edges in G(t)

communi-starting atm i and ending atm j To express this formally, we renumber node,

m i asm1, nodem j asm n, and all nodes on the path between the two nodes cordingly The ability of nodesm1andm nto communicate at a timet can then

ac-be expressed asκ(t, m1,m n) The number of hops needed for the communication

that the links between consecutive hops become available successively withinthe time interval (support for delay tolerant networking) can be expressed as

Each target point can be sensed only by a certain collection of sensor types,denoted by the subsetsY i ⊂ Y It is possible that a target can be sensed by

multiple sensor types However, it is probably not very useful to have targetsthat cannot be sensed by any kind of sensor Therefore, we require thatY iis notthe empty set in this equation Target points outside the region of deployment

R are not allowed.

P Y =p Y1

1 , , p Ym

m |p Yi

i ∈ R ∧ Y i ⊂ Y ∧ Y i = ∅ . (9)

We define the area that is covered by all sensors of a certain type y, at a time

t, as A y(t) In this equation, A v y denotes the area that is, covered by the sensor

of type y of node v The shape of this area can be arbitrary, representing the

Table II Summary of the Criteriac∗∗

portion of alive nodes cl ln,c ln

maximum tolerable latency cl la,c la latencyl , interval t y

service disruption tolerance cl sd,c sd disruptiont sd

sensing range of a sensor This could be, for example, a circle centered atv or a

circle section originating atv.

4.2 Graceful Degradation

If the network is considered not lively according to our definition of network time, it is interesting to know to what degree the lifetime criteria are fulfilled,and which of the criteria is the main reason for the network failure This isbasically an analysis of lifetime bottlenecks, and can therefore be a very usefulguideline when developing or deploying sensor networks, because it indicatesthe areas with the most room or need for improvement

life-Graceful degradation is defined in the context of reliability measures forcomputing systems as the failure-free operation with decreased performancelevel [Beaudry 1978] Most previous lifetime definitions allow for recognizing

a network either as lively or non-functional and the lifetime is calculated cordingly We intend to inherently design our lifetime description to supportgraceful degradation in the context of fault tolerant systems [Li et al 2004;Zhou et al 2005] Soft limits are added to all the single verification parameters

ac-to reflect ranges instead of hard limits [Najjar and Gaudiot 1990]

In particular, the parametersc∗∗(0≤ c∗∗≤ 1) indicate the soft upper boundabove which the network is considered fully functional The measure of inter-est is how good the network fulfills the criteria depending on their respectiveparameters To measure the extent of this performance degradation, a hardlower bound is needed Below this lower bound, the network is considered non-functional For simplicity, the lower bound can be chosen to be zero Of course,

it is also possible to introduce additional parameters cl∗∗ (0 ≤ cl∗∗ ≤ c∗∗ ≤ 1)that indicate a different lower bound

For each criterion, we define two functions.ψ∗∗ indicates how well the terion is fulfilled, resulting in values in the range [0, 1].ζ∗∗ is a measure ofthe quality of the fulfillment of a criterion, depending on the upper and lowerbounds of the corresponding parameter.ζ∗∗(t) ≥ 1 means the criterion is ful-filled perfectly Ifζ∗∗(t) < 0, the criterion is not fulfilled at all Any value in the

cri-range [0, 1] indicates the goodness of the fulfillment For a linear degradationwith an upper bound ofc∗∗ and a lower bound of zero, the amount of fulfill-ment for each criterion can be given by dividingψ∗∗ and the upper boundc∗∗.For linear degradation with a generic lower bound, a formula for calculating

ζ∗∗(t) according to criterion∗∗ is given in Equation 11 (in the following, we onlyprovide the definition and calculation ofψ∗∗for each lifetime criterion∗∗)

4.3 Time-Integrated Criteria

The idea behind time-integrated criteria is that it is often sufficient if the fillment of a requirement is achieved in a certain time interval For example, if50% of the area is covered at one time in the interval, and the remaining 50%

ful-is covered at another time, the time-integrated area coverage ful-is fulfilled, whileclassical area coverage is not The same applies to many other criteria.Therefore, we introduce an additional parametert y

∗∗to accompany all

crite-ria.t y

∗∗indicates the length of the time interval during which the requirements

must be satisfied Ift y

∗∗is set to be zero, the time-integrated criterion equals

the regular criterion

4.4 Criteria

4.4.1 Number of Alive Nodes The portion of alive nodes, including sleeping

nodes, must be greater thanc lntimes the number of existing nodes at any time

To constrain the lifetime of the sensor network to be at most the time of thefailure of the last alive node, this parameter would have to be set such thatone out of the n existing nodes must be alive: c ln = 1/n This has already

been discussed as thebest case for sensor network lifetime in the related work

section

ψ ln(t)= u(t)

4.4.2 Latency For the latency criterion, it is required that at least a

por-tion ofc la packets must have a shorter delay than the prespecified maximum

To constrain the lifetime of the sensor network to be at most the time of thefailure of the last alive node, this parameter... c∗∗≤ 1) indicate the soft upper boundabove which the network is considered fully functional The measure of inter-est is how good the network fulfills the criteria depending on their respectiveparameters